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Abstract

While diffusion MRI promises an insight into white matter microstructure in vivo,
the axonal pathways that connect different brain regions together can only partially
be segmented using current methods. Here we present a novel method for estimating
the tissue composition of each voxel in the brain from diffusion MRI data, thereby
providing a foundation for computing the volume of different pathways in both health
and disease. With the tissue dependent diffusion model described in this thesis, white
matter is segmented by removing the ambiguity caused by the isotropic partial volumes:
both grey matter and cerebrospinal fluid. Apart from the volume fractions of
all three tissue types, we also obtain estimates of fibre orientations for tractography as
well as diffusivity and anisotropy parameters which serve as proxy indices of pathway
coherence.
We assume Gaussian diffusion of water molecules for each tissue type. The resulting
three-tensor model comprises one anisotropic (white matter) compartment modelled
by a cylindrical tensor and two isotropic compartments (grey matter and cerebrospinal
fluid). We model the measurement noise using a Rice distribution. Markov
chain Monte Carlo sampling techniques are used to estimate posterior distributions
over the model’s parameters. In particular, we employ a Metropolis Hastings sampler
with a custom burn-in and proposal adaptation to ensure good mixing and efficient exploration
of the high-probability region. This way we obtain not only point estimates
of quantities of interest, but also a measure of their uncertainty (posterior variance).
The model is evaluated on synthetic data and brain images: we observe that the volume
maps produced with our method show plausible and well delineated structures for
all three tissue types. Estimated white matter fibre orientations also agree with known
anatomy and align well with those obtained using current methods. Importantly, we
are able to disambiguate the volume and anisotropy information thus alleviating partial
volume effects and providing measures superior to the currently ubiquitous fractional
anisotropy. These improved measures are then applied to study brain differences in
a cohort of healthy volunteers aged 25-65 years. Lastly, we explore the possibility of
using prior knowledge of the spatial variability of our parameters in the brain to further
improve the estimation by pooling information among neighbouring voxels.